Problem: Rewrite as a simplified fraction. ${0.6\overline{3} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 63.3333...\\ 10x &= 6.3333...\end{align*}}$ Subtracting the two equations, we have: ${90x = 57}$ ${x = \dfrac{57}{90}} $ ${x = \dfrac{19}{30}} $